Automatic computer simulations of ESR spectra

A versatility of automatic ESR simulation procedures has been developed to obtain high quality of fitting and produce additional information. The following examples are treated: derivation of long-range proton hyperfine coupling constants from unresolved lines; determination of C-13 hf couplings from the naturally abundant isotope satellites; analyzing chemical exchange phenomena with two-sites model; decomposition of superimposed spectra consisting of poorly resolved components. In order to achieve best agreement between calculated and experimental spectra within a reasonable number of iteration cycles, we combined various approaches, like consecutive independent parameter optimization, least-square approach, optimization on ''serpentines'' and optimization of compound parameters. The spectra can be computed both for liquid and solid state samples, for non-oriented, partially oriented and single crystal samples. Second order perturbation formulas are used for the spin Hamiltonian including g- and hyperfine tensors that have isotropic, axial and rhombic symmetry. For chemical exchange the modified Bloch equation for two-site model is used. Various lineshapes, including Lorentzian, Gaussian, mixed, modulation and dispersion distorted forms are applied. Third order parabolic interpolations are used for building up spectra from individual lines. In order to correct sweep non-linearity a third order interpolation converts the spectrum to become equidistant. This procedure can occasionally improve square deviation by an order of magnitudes for well resolved spectra. In the analysis of strongly overlapping superimposed spectra, simultaneous adjustment of two independent experimental spectra can give an exact decomposition. The inclusion of long-range couplings offers highly perfect fitting and allows one to resolve contributions of naturally abundant C-13 isotopes.